The Two Endpoint Homotopies Differ by a Seam Period
The inverse-scale operation required by the reciprocal normalization anomaly has two source-natural endpoint orientations:
Both are right inverses of the scale derivative, but their difference is the
constant total period of g. For a positive exponential anomaly this period
is nonzero, so one homotopy cannot satisfy both endpoint normalizations.
The multi-tower architecture therefore refines from 3+2+1 to 3+2+2+1:
three state towers, two directed construction/defect towers, two
endpoint-oriented homotopy towers, and one seam-period comparison tower.
Research packet:
research/grothendieck/the-two-endpoint-homotopies-differ-by-a-seam-period.md
Exact checker:
research/grothendieck/checkers/check_two_endpoint_homotopy_seam_period.py
The checker passes 5/5 gates.